We introduce a new framework for compressed sensing (CS) in synthetic aperture radar (SAR) imaging in the case of model error. Conventional CS-based autofocus methods solve a joint optimization problem to achieve both model error parameter estimation and SAR image formation simultaneously. Owing to the possibly nonconvex feature of the joint optimization problem, however, these algorithms may get stuck in local optima having large phase errors and thus fail to reconstruct the image. In contrast, we use phaseless measurements and pose imaging as a convex optimization problem. To solve the convex problem, we use the alternating direction method of multipliers-based approach, which is computationally efficient and easy to implement. The results from simulations with both point targets and extended targets validate the effectiveness of the proposed method.
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